Single-particle based helical reconstruction—how to make the most of real and Fourier space

The helical assembly is a fundamental organization principle of biomacromolecules. To determine the structures of helical filaments or tubes has been helped by the fact that many different views of the helical unit are present to reconstruct a three-dimensional image from a single helix. In this review, I present the current state of helical image reconstruction from electron cryo-micrographs by introducing Fourier-based processing alongside real-space approaches. Based on this foundation, I describe how they can be applied to determine the symmetry and high-resolution structure of helical assemblies. In the past, the main structure determination approach of helical assemblies from electron micrographs was the Fourier-Bessel method, which is based on a comprehensive theory and has generated many successful applications in the last 40 years. The emergence of the single-particle technique allowed segmented helical specimens to be treated as single particles, thus rendering new specimens amenable to 3D helical reconstruction and facilitating high-resolution structure analysis. However, helical symmetry determination remains the crucial step for a successful 3D reconstruction. Depending on the helical specimen, Fourier and real-space approaches or a combination of both provide important clues to establish the correct helical symmetry. I discuss recent developments in combining traditional Fourier-Bessel procedures with single-particle algorithms to provide a versatile and comprehensive approach to structure determination of helical specimens. Upon introduction of direct electron detectors, a series of near-atomic resolution structures from helical assemblies have become available. As helical organization is fundamental to many structural assemblies of the cell, these approaches to structure elucidation open up promising capabilities to study the underlying structures at atomistic resolution.